GMAT Ratio and Proportion

RATIO AND PROPORTION Ratio Ratio is a comparison of two quantities of the same kind. It shows the number of times one quantity contains another quantity. The ratio of two quantities is equivalent to the fraction that one quantity is of the other. The ratio of "a" to "b" is written as a: b, read as "a is to b\ and is equal to a/b. In the ratio a: b, 'a' and 'b" are called the terms of the ratio. ‘a’ is called the first term (antecedent) and Lb" is called the second term (consequent). Note: – o

The ratio is an abstract number. Example: If A has 5 apples and B has 7 apples, then the ratio of the number of apples with A to the number of apples with B is 5: 7, which is equal to 5/7.

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Since the ratio a: b is equal to a/b. b cannot be equal to zero.

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If the terms of the ratio have no common factor other than 1, then the ratio is said to be in lowest terms. Example : 6: 15 in lowest terms is 2: 5

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The order of the terms of a ratio is important, since a: b (a/b) is not the same as b: a (b/a).

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If both the terms of the ratio are multiplied or divided by the same non–zero number, then the ratio will not be changed. e.g. 2: 5 is same as 6:;15 (each term multiplied by 3) e.g. 10: 5 is same as 2": 1 (each term is divided by 5)

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Ratio of equality, greater inequality and lesser inequality.

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If the antecedent = consequent (a = b), the ratio is called the ratio of equality. Example : 1 : 1 o

If the antecedent>consequent (a>b). The ratio is called the ratio of greater inequality.

Example : 5 : 2 Note 1 : – In the ratio of greater inequality, (a+ x): (b + x) <

a: b

Example : (5 + 1) : (2 + 1) – 6 : 3 < 5 : 2 Note 2: – In the ratio of greater inequality, (a – x}: (b – x) > a: b Example : (5 – 1): (2 – 1) = 4 : 1 > 5 : 2 o

If the antecedent < consequent, the ratio is called the ratio of lesser inequality.

Example : 1 : 2 Note 1: – In the ratio of lesser inequality, (a + x): (b + x) > a: b Example : (1 + 1) : (2 + 1) = 2 : 3 > 1 : 2 Note 2: – In the ratio of lesser inequality, (a – x): (b – x) < a: b Example : (2 – 1) : (5 – 1) – 1 : 4